10 - TESSELLATIONS

Abstract

This chapter provides an overview of the concept of tessellations. Tiling the kitchen floor or the bathroom wall using tiles of the same square shape is the most elementary example of a tessellation, which is the covering of an area without overlapping or gaps between the tiles. Square or rectangular tiles are the most convenient because the regions to be tiled are usually rectangular, although there might be need to trim the finish tiles to shape the edge of the region. It is possible to tessellate a region using a tile with any quadrilateral shape. The mathematical purpose of this activity is to first see how to describe the position of any one tile with reference to an adjacent tile and then to capture intuitively an awareness of the basic requirements for fitting shapes together in order to tessellate a region. The reasoning that a quadrilateral must tessellate a region by this rotation method is based on the sum of the angles of the quadrilateral being 360°. However, a five-sided figure has an angle sum of 540° and this makes tessellation impossible.